System And Method For Providing Systemic Casualty Reserve Protection

ABSTRACT

A system, method and computer readable storage medium for calculating a first industry index amount at an index year based on selected loss values for the index year for a plurality of companies in a defined line of business and a predetermined number of years preceding the index year for the plurality of companies and loss estimates for a number of years subsequent to the index year corresponding to a predetermined term of a systemic risk product for the plurality of companies, calculating a second industry index amount based on selected loss values for the index year for the plurality of companies, a predetermined number of years preceding the index year for the plurality of companies and at least one year subsequent to the index year and calculating an industry index value based on the first and second industry index amount.

BACKGROUND INFORMATION

A customer of an insurance company or a reinsurance company pays the(re)insurance company a premium to bind a (re)insurance policy for thecustomer. The (re)insurance policy allows the customer to make a claimagainst the (re)insurance company for a covered amount when the customersuffers a loss covered by the (re)insurance policy. The (re)insurancecompany is generally required by law or insurance regulation to keep acertain amount of the premium payment available to pay anticipatedlosses. These funds that are set aside to pay later losses are referredto as loss reserves.

(Re)insurance companies may also hedge their risk on a (re)insurancepolicy by using other financial instruments related to the entire(re)insurance industry, such as CAT bonds or industry loss warranties(“ILWs”). These industry-based or index-based securities generally useindustry losses as a trigger mechanism for payout of a specified amountof money to a (re)insurance company or other insured entity. It is notedthat throughout this description when the term “security” or“securities” is used it refers to the reinsurance or ILW instruments,which may or may not be a security as that term is defined by law. AnILW contract is a manner through which one party will purchaseprotection based on the total loss arising from an event or series ofevents to the entire (re)insurance industry rather than its individualloss. The maximum amount of protection offered by the contract isreferred to as the “limit.” The industry loss threshold whose exceedanceresults in a payment under the contract for as much as the limit isreferred to as the “trigger.” To provide a specific example, aninsurance company may purchase a contract having a limit of $200 millionthat is payable upon an industry loss event of $25 billion (thetrigger). That is, if an event occurs (e.g., an earthquake) where thetotal industry loss exceeds $25 billion, the insurance company willreceive a payment up to a limit of $200 million, regardless of actuallosses suffered by the insurance company during the event.

However, there are no effective instruments that are offered to hedge aninsurance company's risk for casualty lines of business based onsystemic risks, e.g., those risks that are of, relating to, or common tothe entire system and experienced across and entire line of business orthe entire industry. An example of systemic risk is aggregation risk,which is an exposure concentration affecting similar types of risks or aparticular coverage involving multiple accident years arising out of aparticular product, substance or some common causative factor such as adesign, business activity, error or omission. Other examples of systemicrisk include a new legal theory, a new coverage interpretation,liability arising out of a relatively new or existing product ortechnology, changes in the macroeconomic conditions (e.g., medicalinflation driven by a costly new technology or unforeseen cost shiftsassociated with universal health insurance), changes in the regulatoryenvironment or other unforeseen causes that affect the entire industry.

There are several reasons that these security products do not exist todeal with systemic risk, including moral hazard (e.g., the hazardassociated with the individual company's ability to manipulatereserves), high capital charges associated with the long tailed (slow tosettle) lines of business (make it uneconomic for reinsurers to write),and significant underwriting expense and due diligence and marketreservations to write casualty due to external factors including social,economic and political influences.

SUMMARY OF THE EXEMPLARY EMBODIMENTS

A first exemplary embodiment is directed to a method for calculating afirst industry index amount at an index year based on selected lossvalues for the index year for a plurality of companies in a defined lineof business and a predetermined number of years preceding the index yearfor the plurality of companies and loss estimates for a number of yearssubsequent to the index year corresponding to a predetermined term of asystemic risk product for the plurality of companies; calculating asecond industry index amount based on selected loss values for the indexyear for the plurality of companies, a predetermined number of yearspreceding the index year for the plurality of companies and at least oneyear subsequent to the index year and calculating an industry indexvalue based on the first and second industry index amount.

A second exemplary embodiment is directed to a system having a memorystoring a set of instructions and a processor executing the set ofinstructions to perform a method. The method including calculating afirst industry index amount at an index year based on selected lossvalues for the index year for a plurality of companies in a defined lineof business and a predetermined number of years preceding the index yearfor the plurality of companies and loss estimates for a number of yearssubsequent to the index year corresponding to a predetermined term of asystemic risk product for the plurality of companies, calculating asecond industry index amount based on selected loss values for the indexyear for the plurality of companies, a predetermined number of yearspreceding the index year for the plurality of companies and at least oneyear subsequent to the index year and calculating an industry indexvalue based on the first and second industry index amount.

A further exemplary embodiment is directed to a non-transitory computerreadable storage medium comprising a set of instructions that areexecutable by a processor to perform a method. The method includingcalculating a first industry index amount at an index year based onselected loss values for the index year for a plurality of companies ina defined line of business and a predetermined number of years precedingthe index year for the plurality of companies and loss estimates for anumber of years subsequent to the index year corresponding to apredetermined term of a systemic risk product for the plurality ofcompanies, calculating a second industry index amount based on selectedloss values for the index year for the plurality of companies, apredetermined number of years preceding the index year for the pluralityof companies and at least one year subsequent to the index year andcalculating an industry index value based on the first and secondindustry index amount.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an exemplary derivation of a cumulative payment pattern(labeled % Paid) and incremental payment pattern (labeled Δ% Paid) usinga 2-year weighted average paid chain ladder method. The estimatecorresponds to index year 2000. The payment patterns and the lossamounts used in their derivation serve as inputs into the calculation ofthe index.

FIG. 2 shows an exemplary initial index based on projected payments overthe next five calendar years using the data from FIG. 1 for the indexyear 2000.

FIG. 3 shows an exemplary updated index one year forward based onupdated actual payments for the next calendar year and projected initialpayments for the next four calendar years following the next year usingthe data from FIG. 1 for the index year 2000. Other interim values ofthe index would be based on the same procedure but would include moreyears of actual payments. For example, the index two years forward wouldbe based on two calendar years of actual payments and three years ofprojected payments (as originally calculated).

FIG. 4 shows an exemplary final value of the index based on updatedactual payments after five years for the index year 2000.

FIG. 5 illustrates an exemplary method for implementing the exemplarysystemic risk product.

FIG. 6 shows a gross paid loss table that has gross paid loss valuesfrom various annual reports and an incremental paid loss table that iscalculated from the gross paid loss table.

FIG. 7 illustrates a table showing gross premiums that correspond to thesame time periods as the gross loss paid values in the gross paid losstable of FIG. 6.

FIG. 8 shows a first table illustrating unadjusted age-to-age factorsbased on the gross paid loss table values of FIG. 6 and a second tableillustrating adjusted age-to-age factors based on an adjustmentcalculation.

FIG. 9 shows an adjusted gross paid loss table based on the gross paidloss table of FIG. 6 and the adjusted age-to-age factors of FIG. 8.

FIG. 10 shows an adjusted incremental paid loss table based on theadjusted gross paid loss table of FIG. 9.

FIG. 11A shows a first portion of exemplary calculated default factorsfor use when observed factors fail consistency checks.

FIG. 11B shows a second portion of the exemplary calculated defaultfactors for use when observed factors fail consistency checks, asillustrated in FIG. 11A.

DETAILED DESCRIPTION

The exemplary embodiments may be further understood with reference tothe following description of the exemplary embodiments and the relatedappended drawings, wherein like elements are provided with the samereference numerals. The exemplary embodiments are related to systems andmethods for providing systemic casualty reserve protection.Specifically, the exemplary embodiments provide a product based on anindustry index to hedge against systemic risk (hereinafter referred toas the “systemic risk product”). The following will provide adescription of the systemic risk product, a manner of calculating theproprietary industry index, and a manner of calculating the payoff ifthe trigger is satisfied subject to the other terms and conditions ofthe systemic risk product.

Throughout this description it will be described that an insurancecompany will be the purchaser of the systemic risk product to hedge itsrisk against systemic risk. However, those skilled in the art willrecognize that other entities may also be the purchaser of the systemicrisk product. For example, as described above, reinsurers may have thesame issues as insurance companies, thus, a reinsurer may be thepurchaser of the systemic risk product. In another example, a companymay self insure against certain risks. This company may be the purchaserof the exemplary systemic risk product. Thus, it should be understoodthat the term “insurance company” is not limited to the traditionaldefinition of that term. As will be noted below, the exemplary systemicrisk product may be in the form of a reinsurance product or an ILWproduct. Thus, throughout this description, where the term “reinsurer”is used, it is meant to refer to any entity that is the seller of theexemplary systemic risk product, not only entities that engage in thereinsurance business as that business is understood by those skilled inthe art.

Insurance companies use various actuarial techniques to estimate theirpaid losses for upcoming calendar years. These techniques may include,for example, chain ladder models, generalized linear models (GLM's),etc. Based on these techniques, the insurance companies estimate and setaside the proper loss reserves to eventually pay out for any actuallosses suffered by the insured parties. Empirical data indicates thatcalendar year trends for actual paid losses tend to be cyclical and thatall insurance companies in a particular line of business tend to move intandem. While there is always the possibility of outliers, e.g., aparticular insurance company has written policies that suffer lossesbased on a particular event while another insurance company does nothave exposure to a particular event, etc., the data supports theproposition of the general rule that losses in individual lines ofbusiness tend to move in the same direction for all companies writingpolicies in that line of business. This leads to a conclusion thatsystemic losses that are spread throughout the entire industry willimpact an individual company. These systemic losses cannot be accountedfor by the actuarial techniques because the data relating to suchsystemic losses is not typically observed in the historical data becausethe data does not capture unforeseen and/or extremely rare events. Someexamples of systemic risk or causes of systemic losses were providedabove. The particular reason for a systemic loss is not important,because in most cases, it is not foreseeable and therefore cannot bebuilt accurately into the models. Most insurance companies know orintuitively know that the systemic risk exists and desire to hedge theirexposure to the risk. However, as described above, there is nowell-designed synthetic product available for such a hedge.

The exemplary systemic risk product described herein provides amechanism for an effective hedge against adverse developments in unpaidlosses driven by systemic shocks to the system or the industry as awhole. Thus, the purpose of the systemic risk product is to protect theinsurance company against systemic events, not firm specific risk. Forthis reason, the systemic risk product is based on an industry index,e.g., a plurality of companies that represent the industry. The industryindex may be generally described as a ratio of actual paid lossesagainst projected paid losses, although other data points may be used.An exemplary calculation of an index is provided below.

It has been found that the industry development trends have betterpredictability than an individual insurance company's developmenttrends. Further, the industry index based on paid loss data eliminatesthe moral hazard associated with any individual company's reservingpractices, e.g., the carried reserves of any individual company do notinfluence the systemic risk product.

Each insurance company is required to file a Schedule P for its line ofbusinesses that includes paid loss data. Thus, the index that is usedfor the exemplary systemic risk product described herein is based onpublicly available paid loss data for each of the insurance companies inthe index. Since all the underlying data for the calculation is publiclyavailable data, the calculation is verifiable, transparent and there islittle or no due diligence required on individual companies, therebyexpediting the process.

In general, the industry index that is used for the exemplary systemicrisk product described herein does not require a calculation to beperformed for each insurance company. Once the index has been calculatedand verified, the same index may be used for any insurance companywishing to purchase a cover for the line of business for which the indexwas calculated. It should be noted that the industry index is flexibleand may be modified to improve the hedge for individual insurancecompanies or groups of insurance companies. In one example, the paidloss data used to calculate the index may be gross paid loss data,whereas in another example the paid loss data may be net paid loss data.In a further example, a specific insurance company may have certainoverweight geographical exposures (e.g., California, Illinois andFlorida), the industry index may be modified to more closely match thisgeographical overweight exposure of the insurance company to improve thehedging effect of the systemic risk product.

Those skilled in the art will understand that the Schedule P filing hasten (10) years worth of paid loss data. Thus, the exemplary calculationprovided below shows the calculation based on the most current ten (10)years of publicly available paid loss data based on the Schedule Pfilings. However, historical years may be retained such that more thanten (10) years of data may be used in the calculation. Another point offlexibility of the systemic risk product is that it may have any termfrom 1-9 years. The exemplary calculation provided below will assume aterm of five (5) years, but the term could also be 2 years, 3 years, 7years, etc.

The exemplary systemic risk product that is based on the indexcalculation may be a reinsurance product and/or an ILW product. Theexemplary calculation provided below will be for a reinsurance product,but characteristics of an exemplary ILW product will also be provided. Ageneral description of the systemic risk product is a synthetic adversedevelopment cover that includes an accelerated formulaic mandatorycommutation feature allowing for commutation after a defined term of 1-9years. As described above, the systemic risk product is based on anindustry index calculated from Schedule P paid loss data and is designedto cover the systemic contribution to company adverse development.

The exemplary methods of calculating the industry index and thecorresponding payoffs for the systemic risk product that are describedbelow may be advantageously implemented using one or more computerprograms executed on a computer system having a processor or centralprocessing unit, such as, for example, a computer using an Intel-basedCPU, such as a Pentium or Centrino, running an operating system such asthe WINDOWS or LINUX operating systems, having non-transitory storagemediums, such as, a hard drive, RAM, ROM, a compact disc,magneto-optical storage device, and/or fixed or removable media, andhaving a one or more user interface devices, such as, for example,computer terminals, personal computers, laptop computers, and/orhandheld devices, with an input means, such as, for example, a keyboard,mouse, pointing device, and/or microphone. The methods may also beimplemented via a server executing a computer program and having usersremotely access the results generated by the server for display on theirpersonal devices, e.g., over the Internet, a company intranet, cloudcomputing devices and/or services, etc.

The following provides an exemplary index calculation and reinsurancesystemic risk product based on a worker's compensation line of business.In this example, ABC insurance company has a $500M portfolio of workerscompensation reserves and the company's management wants coverage for asystemic shock on these reserves. Thus, a reinsurer will develop asystemic risk product for the workers compensation line of business bycalculating an industry index and negotiating and/or offering severalother terms to ABC insurance company, which will be described below. TheABC insurance company may then elect to purchase the systemic riskproduct for the workers compensation line of business.

In this example, the exemplary index provided below is based onthirty-six (36) large workers compensation insurance writers that madeup 60% of the industry based on premium volume in 2009. From thisexample, it can be seen that the index is based on a substantial number(but not all) of companies in the industry. There is no specificthreshold of a required number of companies or premium volume within theindex, but it should be clear that the higher the number and/or volumewithin the index, the more accurate the index will be for the purpose ofhedging against systemic risk. Also, while the example used throughoutthis description is based on the workers compensation line of business,the exemplary embodiments may be applied to any Schedule P defined lineof business, e.g., homeowners insurance, private passenger auto, medicalmalpractice, other liability occurrence, etc.

The commutation amount of the systemic risk product is calculated basedupon the final value of the industry index and the paid losses of ABCinsurance company. In this example, it is considered that the partieshave negotiated a limit of $200M and a retention of $600M. In thescenario of the reinsurance systemic risk product, the parties have alsonegotiated a dual trigger and corresponding values to activate thecover. In this example, ABC insurance company reserves must develop by$50M (10% of the $500M reserve described above) and the index value atyear 5 expressed as a ratio to the initial index value must exceed anindex trigger of 1.10. The index trigger and an exemplary manner ofcalculating the index trigger value are described below.

In this example, the estimation of the outstanding losses for payment atcommutation (e.g., end of the defined 5 year term) is based on the indexyear 2000. The selection of the year 2000 is merely for illustrativepurposes and any index year may be selected. The formula for outstandingloss or commutation amount (CA) in the layer based on theabove-described parameters is calculated as follows:

CA=Min(Max(I(5)−1.1, 0), 0.1)×$2B

where,

-   -   I(5) is the index value at year 5 expressed as a ratio to the        initial index value (as described above, the exemplary systemic        risk product has a selected term of 5 years in this example),        the value 1.1 is based on the negotiated index trigger point of        1.1,    -   the value 0.1 is the negotiated index limit, and the $2B value        is a scalar that is negotiated to convert the index value to a        monetary value.

Exemplary calculations using this formulas will be provided below. Thoseskilled in the art will understand that the values and parameters usedabove are only exemplary and that different sellers and/or buyers of asystemic risk product may use and/or negotiate different values andparameters.

FIG. 1 shows an exemplary 2-year weighted average paid chain ladderestimate triangle 100 for the index year 2000 as described above. Thisexemplary data will be used to show an exemplary calculation of theindustry index on which the systemic risk product is to be based. Again,it is noted that using a 2-year weighted average is only exemplary andother time frames and method may also be used, e.g., 3-year weightedaverage, 5-year straight average, etc. Initially, the column 105 showsthe accident years from 1989-2000 and the row 110 shows the developmentyears from year 1-10. The values in the triangle 100 represent theactual cumulative paid loss values for the business line as of December31, 2000, e.g., workers compensation. For example, for accident year1998, after development year 1 (December 31, 1998), a cumulative total173 of $2,986,866 has been paid, after development year 2 (December 31,1999), a cumulative total 171 of $6,606,706 has been paid and afterdevelopment year 3 (December 31, 2000) a cumulative total 179 of$8,825,324 has been paid. In another example, for accident year 1993,after development year 6 (December 31, 1998), a cumulative total 191 of$13,487,296 has been paid, after development year 7 (December 31, 1999),a cumulative total 192 of $13,923,433 has been paid and afterdevelopment year 8 (December 31, 2000), a cumulative total 193 of$14,253,401 has been paid. As described above, the values in this upperleft portion 115 of the triangle 100 are actual cumulative paid lossvalues that have been extracted from Schedule P filings for a number ofinsurance companies in the workers compensation line of business. Asdescribed previously, in this example, the values are based onthirty-six (36) workers compensation insurance writers that made up 60%of the industry based on premium volume in 2009.

As shown in FIG. 1, the bottom right portion 117 is the forecast periodfor which there are no actual paid values at this time (assuming it isDecember 31, 2000). The calculation of these forecast values that willbe filled in the bottom right portion 117 will be discussed in greaterdetail below.

FIG. 1 also includes a table 120 that shows an age-to-age (ATA) factor130, an age-to-ultimate (ATU) factor 140, a cumulative percentage paidfactor 150 and an incremental percentage paid factor 160 for each of thecorresponding development years. Each of these factors and thecalculation of their corresponding values 130-160 will be described. TheATA factor 130 is the change in payments made on a defined set of claimsbetween successive points in time. In this example, this change ismeasured based on a two-year weighted average of successive accidentyears and successive development years. For example, the first ATAfactor value 131 of 2.27063 is calculated by adding the values for thesecond year of development of accident year 1998 (value 171 of6,606,706) and accident year 1999 (value 172 of 7,061,371) to give atotal of 13,668,077. Then, the values for the previous (first) year ofdevelopment of accident year 1998 (value 173 of 2,986,866) and accidentyear 1999 (value 174 of 3,032,646) are added resulting in the summedvalue of 6,019,512. The first summed value is then divided by the secondsummed value to calculate the ATA factor value 131(13,668,077/6,019,512=2.27063). A second exemplary calculation of theATA factor value 132 will be performed to provide a further example. Inthis example, the values for the sixth year of development of accidentyear 1994 (value 175 of 11,793,143) and accident year 1995 (value 176 of10,498,280) are summed to give a total of 22,291,423. Then, the valuesfor the previous (fifth) year of development of accident year 1994(value 177 of 11,260,574) and accident year 1995 (value 178 of10,017,405) are added resulting in the summed value of 21,277,979. Thefirst summed value is then divided by the second summed value tocalculate the ATA factor value 132 (22,291,423/21,277,979=1.04763). Theremaining ATA factors 130 may be calculated in the same manner.

The ATU factor 140 is the cumulated ATA factors 130. In this example, itis considered that the ultimate payment amount occurs at year 10 ofdevelopment, e.g., there is no paid development after year 10. Thus, theATU factor value corresponding to development year 10 is unity as shownby the ATU factor value 141. The remaining ATU factor 140 values for anydevelopment year may be calculated by multiplying the ATA factor 130value of the development year of interest by the ATU factor 140 value ofthe next development year. Thus, to calculate the ATU factor value 142of 1.01339 for development year 9, the ATA factor value 133 of 1.01339of the same development year is multiplied by the ATU factor value 141of 1.00000 of the next development year 10, resulting in the ATU factorvalue 142 of 1.01339. To provide a further example, the ATU factor value143 of 1.41203 for development year 3 is calculated by multiplying theATA factor value 134 of 1.14676 of development year 3 by the ATU factorvalue 144 of 1.23132 of development year 4. Again, the remaining ATUfactors may be calculated in the same manner.

The cumulative percentage paid factor 150 is the cumulative percentageof the amount paid in the development year against the projectedultimate cumulative amount paid. Thus, the amounts paid in developmentyear 1 are projected to be approximately 23.5% (0.23503) of the ultimatecumulative paid amount. The cumulative amounts paid through developmentyear 2 are projected to be approximately 53% (0.53366) of the ultimatecumulative paid amount. The cumulative paid factor at each report is thereciprocal of the ATU Factor; that is, it is calculated by dividing oneby the ATU factor.

The incremental percentage paid factor 160 is the difference fromdevelopment year to development year in the cumulative percentage paidfactor 150. Thus, as described above, the percentage paid factor valuesfor development years 2 and 1 are 0.53366 and 0.23503, respectively.Subtracting the value of development year 2 from the value ofdevelopment year 1 results in (0.53366−0.23503=0.29863) which is thevalue for development year 2 for the incremental percentage paid factor160. Again, the remaining incremental percentage paid factor 160 valuesmay be calculated in the same manner.

The meaning of the exemplary data presented by the triangle 100 andtable 120 will be described. In an example, accident year 1995 isselected. Through the sixth development year, a cumulative total of$10,498,280M has been paid as shown by value 176. This cumulative paidvalue 176 represents approximately 92.07% of the cumulative paid lossprojected through development year 10 as shown by the value 182. Indevelopment year 6, approximately 4.186% of the ultimate cumulative paidloss will be paid as shown by the value 184.

FIG. 2 shows an exemplary initial index based on projected payments overthe next five calendar years using the data from FIG. 1 for the indexyear 2000. Initially, it can be seen that the data presented in table200 is incremental paid loss data rather than cumulative paid loss dataas shown in FIG. 1. The actual incremental paid loss data is shown asdata 210 and may be calculated using the cumulative paid loss datapresented in FIG. 1. The calculation is performed, for each accidentyear, by subtracting the cumulative paid loss in previous developmentyear from the current development year thereby resulting in theincremental paid loss for the current development year. To provide anexample, to calculate the incremental paid loss value 212 of 4,028,725for accident year 1999, development year 2, the cumulative paid lossvalue 174 for accident year 1999, development year 1, is subtracted fromthe cumulative paid loss value 172 for accident year 1999, developmentyear 2 (7,061,371−3,032,646=4,028,725). The remaining incremental values210 may be calculated in the same manner.

The table 200 also includes the projected incremental paid loss data 220over the next five years. For example, the actual paid loss data foraccident year 2000 only includes development year 1. However, projectedincremental paid loss data for development years 2-6 is also included.As noted above, the projected incremental values may be calculated forany number of years from 1-9 for the purposes of the index, but in thisexample, the number of years has been selected to be five to match theterm of the contract in this example. This projected paid loss data iscalculated based on the data from FIG. 1 and illustrated in table 250 ofFIG. 2. For example, as shown in table 250, for accident year 2000(column 251), the cumulative paid loss from the latest report(development year 1, column 252) is 3,135,073 (column 253). Thisrepresents a cumulative percentage paid 150 value of 23.503% of thetotal projected paid loss through development year 10 (column 254).Dividing the cumulative percentage paid 150 by the latest reportedcumulative paid loss results in the cumulative projected paid lossthrough the tenth development year (column 255). In this example, thecalculation is 3,135,073/0.23503=13,339,181. The cumulative projectedpaid loss value through the tenth report may then be multiplied by theincremental percentage paid factor 160 value for any development year toresult in the projected incremental paid loss value for that developmentyear. Continuing with the example of accident year 2000, the cumulativeprojected paid loss of 13,339,181 may be multiplied by the incrementalpercentage paid factor 160 value of 0.298633 for development year 2 toresult in (13,339,181×0.298633=3,983,514) which is the incremental paidloss value 222 for accident year 2000, development year 2. The remainingprojected incremental paid loss values 220 for other accident anddevelopment years may be calculated in the same manner as shown in table250.

It is noted that table 200 also includes the incremental projectedlosses 230 for further years. These values were provided to complete thetable, but are not necessary because, as stated above, it has beenselected in this example to use the term of five years for the cover. Itis also noted that the above calculations and further calculationspresented below may include some rounding errors if it is attempted toreproduce these calculations from the values presented in FIGS. 1 and 2.These rounding errors add an insignificant amount of error to thecalculations and do not affect the general intent of the index.

The table 250 also includes the base forecast 260 for the index. Thebase forecast 260 is the total projected payments over the next fivecalendar years for the most recent nine accident years. This value iscalculated by summing the projected incremental paid losses 220 for eachaccident year through five calendar years as shown in column 257 andthen summing all these values. For example, for accident year 1993,there are two development years of projected incremental losses shown asvalues 224 (228,510) and 226 (193,924), the sum of which is 422,434 asshown in column 257 of table 250. The summation of each of the calendaryears results in the base forecast 260 value of 23,475,906. The indexcan be expressed as a ratio to the base forecast. Thus, the index isinitially unity by construction. The base forecast 260 is considered tobe the index value I(0)=1. The purpose of this index value will bedescribed in greater detail below.

FIG. 3 shows an exemplary updated index based on updated actual paymentsand projected payments over the next four calendar years using the datafrom FIG. 1 for the index year 2000. Thus, in this example, it is time 1year or the end of 2001 (December 31, 2001). At this time, the actualpaid losses 310 for calendar year 2001 have been added to the table 300.The remaining projected paid losses 320 are the same as the projectedpaid losses 220 from table 200.

The actual paid losses 310 from calendar year 2001 are different fromthe projected paid losses that were shown in table 200. Therefore, thesummation of the actual paid losses for calendar year 2001 and theprojected paid losses for the next four calendar years can bere-performed as shown in table 350. As shown, the summation for thisupdated forecast is the value 360 of 23,996,090, which is greater thanthe original base forecast 260 of 23,475,906. This updated forecastexpressed as a ratio to the base forecast is the index value at year 1I(1). I(1)=23,996,090/23,475,906=1.022. As each successive calendar yearpasses, a new index value may be calculated in a similar manner as aratio to the base forecast 260.

FIG. 4 shows an exemplary updated index based on updated actual paymentsafter five years for the index year 2000. The table 400 is for time 5years or the end of 2005 December 31, 2005). At this time, the actualpaid losses 410 that correspond to the original projected paid losses220 have occurred such that the actual values 410 are shown in table400. Therefore, the summation of the actual paid losses for the 5 yearsmay be performed as shown in table 450 resulting in the updated forecast460 value of 27,130,311. Thus, since the exemplary product has a timehorizon of five years, a Settlement Value of the index may bedetermined. The Settlement Value is the index value at year 5 expressedas a ratio to the base forecast, I(5), calculated in the same manner asdescribed above, i.e., I(5)=27,130,311/23,475,906=1.156.

Now that the exemplary five years have expired, an exemplary commutationcan be provided. It will be assumed that the conditions of thereinsurance contract have been met, e.g., the ABC insurance companyreserves developed adversely from $500M to $700M, thus meeting thecondition of a mimimum $50M or 10% adverse development. In addition, ascalculated above, the index value at year 5, I(5), exceeds the conditionof being greater than an trigger point value of 1.1. As should be clear,if either or both of these conditions have not been satisfied, nocommutation or payoff will be due ABC insurance company. However, thisexample has been provided to show how a commutation may be paid to ABCinsurance company based on the purchased systemic risk product. It willalso be assumed that the ABC insurance company has paid zero in thelayer $200M excess of $600M. Otherwise, the Commutation Amount would bereduced for any loss recoveries that have already been made. TheCommutation Amount (CA) may then be calculated using the formulaprovided above as follows:

CA=Min(Max(I(5)−1.1, 0), 0.1)×$2B

where, in this example,

I(5)=1.156

Index Trigger=1.1

Max (1.156−1.1,0)=0.056

Min (0.056, 0.1)=0.056

Company Paid in Layer=0

CA=0.056×$2B=$112M

Therefore, in this exemplary embodiment, if ABC insurance company hadpurchased the systemic risk product based on the index as describedabove, and the losses developed in the exemplary manner described above,ABC insurance company would be entitled to a payoff of $112M after year5.

As described above, the provided example is based on a reinsuranceproduct. A similar ILW product may also be provided and calculated inthe same manner described above for the reinsurance product. The normaldifference between the reinsurance product and the ILW product is thatthe ILW product would typically not include the attachment limit (e.g.,$200/$600) or the condition of adverse development on the purchaser ofthe cover and commutation amount will be based on:

CA=Min(Max(I(5)−1.1, 0), 0.1)×$2B

Those skilled in the art will understand that the above-describedexemplary embodiments may be implemented in any suitable software orhardware configuration or combination thereof. An exemplary hardwareplatform for implementing the exemplary embodiments may include, forexample, an Intel x86 based platform with compatible operating system, aMac platform and MAC OS, etc. In a further example, the exemplaryembodiments of the systems and methods for comparing company losses toindustry indices may be a program containing lines of code stored on anon-transitory computer readable storage medium that, when compiled, maybe executed on a processor.

FIG. 5 illustrates an exemplary method 500 for implementing theexemplary systemic risk product. In step 510, an exemplary industryindex for a selected index year is calculated based on the actual paidloss data from the Schedule P filings of the insurance companies thatare included in the industry index. However, it is noted that the indexis not limited to being calculated based on the actual paid loss, butmay also be calculated based on other data reported in the Schedule Pfilings, e.g., case incurred loss, etc. The calculations of the industryindex for exemplary index year 2000 were described above with referenceto FIGS. 1 and 2. The industry index is based on the actual paid valuesand the paid estimates for the term of the systemic risk product. Asdescribed above, the base factor 260 that corresponds to an index valueI(0)=1 is calculated.

In step 520, the index value at the latest reported year is calculated.In the example above, FIG. 3 and the related description describecalculating the index value I(1) for the latest reported year using theactual paid values for the latest reported year and the originalprojected values for the remainder of the term.

In step 530, it is determined whether the latest reported year was theterm year. If the latest reported year was not the term year, the methodloops back to step 520 to calculate the index value for the nextreported year when that data becomes available. If the latest reportedyear was the term year, for example, the index value I(5) for a term of5 years as calculated above with reference to FIG. 4, the methodcontinues on to step 540.

In step 540, the commutation amount (CA) is calculated using the formulaprovided above. As described above, the values provided in the formulaare based on the industry index and some values are based on values thatare negotiated between the reinsurer and the insurance companypurchasing the systemic risk product. As also described above, thecommutation amount assumes that all other terms of the systemic riskproduct have been met (e.g., the dual triggers of the exemplaryreinsurance product have been met).

An exemplary system may perform the steps of method 500. The exemplarysystem may comprise a receiving arrangement having hardware, software ora combination thereof that may, for example, receive the data necessaryfor performing the calculations of steps 510-540. The same system mayalso comprise a calculating arrangement having hardware, software or acombination thereof that may, for example, perform the calculationsdescribed with reference to steps 510-540. It is noted that theabove-described arrangements are only exemplary and that the variousarrangements may have its functionalities combined into a singlecomponent or distributed to multiple components. For example, thereceiving arrangement and calculating arrangement may be implemented viathe same computer code being executed on the same processor.

Throughout this description, it has been described that values fromSchedule P for multiple insurance companies are used in the variouscalculations. However, since the values that are used in thecalculations are spread out over multiple years of the reports, theremay be inconsistencies between various years. The inconsistencies may bethe result of, for example, mergers, acquisitions, rehabilitation,liquidation, distortions due to inter-company pooling or the insurancecompany's data clearly appears to be seriously distorted for reasonsthat are not readily apparent. Thus, the exemplary embodiments provide aseries of rules for adjusting the inconsistencies.

FIGS. 6-10 illustrate a first example of an inconsistency correction.Initially, FIG. 6 shows a gross paid loss table 600 that has gross paidloss values from various annual reports. These values are used tocalculate an incremental paid loss table 610. To provide a specificexample, a gross loss value 602 (521) that is from a first annual reportis subtracted from a gross loss value 604 (3,435) that is from adifferent annual report to result in the calculated incremental lossvalue 612 (2,914). Thus, for the calculation to be meaningful, thevalues taken from various annual statements should be consistent.

In one example, inconsistencies among annual statements may bedetermined based on gross premiums. For example, FIG. 7 illustrates atable 700 showing gross premiums on December 31, 2004 that correspond tothe same time periods as the gross loss values in table 600. As shown bythis table 700, there is a slight inconsistency between 2003 and 2004Annual Statements for accident year 2002. Specifically, the value 705 is7,140 while the value 710 is 6,962. A factor can be calculated bydividing the value 710 by the value 705 resulting in(6,962/7,140=0.975). In this example, it has been determined thatpremium factors that fall within a tolerance level of 0.95 to 1.05 areconsidered minor inconsistencies that can be mechanically adjusted asdescribed below. The range will be subject to negotiation.

An exemplary rule of applying a paid loss ratio development value isapplied if the premium change is within the tolerance range (e.g.,+/−5%). In this example, referring to table 600, the calculated 2nd to3rd factor for accident year 2002 gross paid loss is the value 604divided by the value 602 or 3,435/521=6.593. However, based on the ruledescribed above, the paid loss ratio age-to-age factor is used as aproxy for the paid loss age-to-age factor. In this example, this valueis calculated as: (gross paid loss value 604/premium value 710)/(grosspaid loss value 602/premium value 705) or(3,435/6,962)/(521/7,140)=6.762. Equivalently, the original developmentfactor of 6.593 may be adjusted by dividing it by the premium adjustmentof 0.975 (6.593/.975=6.762), yielding an adjusted development factor of6.762.

FIG. 8 shows a table 800 that includes the age-to-age factors beforeadjustments, including the unadjusted age-to-age factor 805 (6.593) ascalculated above. FIG. 8 also shows a table 810 that includes theage-to-age factors after adjustments, including the adjusted age-to-agefactor 815 (6.762) as calculated above.

FIG. 9 shows the adjusted gross paid loss table 900 including theadjusted gross loss value 910 (3,523). As can be seen from the figures,the table 900 is identical to the table 600, except for the adjustedgross loss value 910. This value 910 is calculated by multiplying theprevious year gross loss value 905 by the adjusted age-to-age factor 815calculated above or 521×6.762=3,523.

FIG. 10 shows an adjusted incremental paid loss table 1000 including anadjusted incremental paid loss value 1010 (3,002). As can be seen fromthe figures, the table 1000 is identical to the table 610, except forthe adjusted incremental loss value 1010. This value 1010 is calculatedbased on the adjusted gross loss value 910 minus the gross loss value905 or 3,523−521=3,002. Thus, the above calculation shows one example ofa rule for dealing with inconsistencies in annual reports.

The above example provided a rule if the inconsistency was within thetolerance range (e.g., +/−5%). The following example provides a rule forcorrecting an inconsistency that is greater than the tolerance range.Most of the companies or “combos” in the index are actually groups ofaffiliated companies. For example, combo 70 is the Travelers Group ofCompanies for which a consolidated annual statement is filed. Wheneverpossible, we make use of the consolidated group annual statements. Inthis example, for simplicity of explanation, it is considered that thegroup of companies filing a consolidated annual statement only consistsof two companies, Company A and Company B. Those of skill in the artwill understand that the principles of correcting for theinconsistencies described below may be extended to groups that arelarger than two companies. In this example, the group accident year 2011premium on annual statements 2011 is $500M and the group accident year2011 premium on annual statements 2012 is $530M. Thus, this 6%discrepancy exceeds the example tolerance of +/−5%. Since the premiumconsistency check for the consolidated (group) annual statements fails,the same consistency check is applied to each individual company in thegroup. A weight is assigned to each company in the group based on thepercentage of loss relative to that of all companies in the group. Thisresults in a rule that if the combined weight of the matching companiesin the group totals less than 90% of the “sum of the pieces”, theage-to-age factor is flagged for later adjustment. An example of thisprocess is provided below.

Again, in this example, there are only two companies in the group.Company A accident year 2011 premium on annual statement 2011 is $460Mand accident year 2011 premium on annual statement 2012 is $450M.Company A passes the premium consistency check since the discrepancy isless than the exemplary 5%. Company A is a “matching” company. Company Aaccident year 2011 Paid Loss on annual statement 2011 is $46M andaccident year 2011 Paid Loss on annual statement 2012 is $85.5M. Thus,the Company A development factor is (85.5/450)/(46/460)−1.9000.

Company B accident year 2011 premium on annual statement 2011 is $50Mand accident year 2011 premium on annual statement 2012 is $85M. CompanyB accident year 2011 Paid Loss on annual statement 2011 is $5M andaccident year 2011 Paid Loss on annual statement 2012 is $17M. Note thatCompany B premium changes by 70%, which exceeds the exemplary 5%tolerance. Since Company B fails the premium consistency check, we donot need to calculate the development factor. Company B is not amatching company.

The weight for Company A is determined based on dividing the Company A2011 Paid Loss on annual statement 2011 by the sum of Company A and B2011 Paid Loss on annual statement 2011 or $46/($46+$5)=90.2%. Since thecombined weight of the matching companies in the group totals at least90% (threshold subject to negotiation) of the “sum of the pieces”, theage-to-age factor is not flagged for later adjustment. A default1st-to-2nd factor for this group is calculated to be 2.02495. Thecalculation of this factor is explained in more detail below. The deemed1st-to-2nd factor is then calculated by multiplying the Company A weightby the Company Development factor and then adding the product of (1—theCompany A weight) times the default 1st-to-2nd factor or90.2%×1.900+(1-90.2%)×2.02495=1.912.

Again in this example, suppose that 1^(st) report paid loss for thegroup as reported on the 2011 annual statement is $52 million. Applyingthe 1.912 factor derived above to $52 million 1^(st) report loss yields$99.424 million—which we deem to be the actual accident year 2011 paidloss at a 2^(nd) report. This figure may not equal the amount actuallyreported on the 2012 annual statement.

In another example, the observed consolidated factor fails consistencycheck and the combined weight of the matching companies in the grouptotals less than 90% of the “sum of the pieces” In this case, theage-to-age factor cannot be calculated accurately and the deemeddevelopment factor will be based on a default factor. This example willbe described with reference to FIGS. 11A and 11B that show a table 1100incorporating the described calculations. For each accident year and agea weighted average age-to-age factor is calculated across all companiesin the basket using only the un-flagged factors. A default age-to-agefactor for each company at each age is then calculated by applying thenegotiated adjustment factors (from a table) to the base weightedaverage factor. The table lists report adjustment factors for thecompanies in the index. Although the factors are subject to negotiation,they are intended to capture idiosyncratic development for each comborelative to industry development. Column (5) 1125 lists the negotiatedadjustment factors for the entities (combos of column (1) 1105).

For example, Combo 70 (as shown in row 1150) has a first reportAdjustment Factor of 0.81 (column (5) 1125). This means that it isexpected that the 1^(st)-to-2^(nd) development factor for Combo 70 to beabout 81% of the industry factor; that is, historically, Combo 70'sfirst report factor has been approximately 81% of the industry factor.Suppose the accident year 2011 weighted average 1st-to-2nd factor turnsout to be 2.5000. As described above, only groups of companies that arenot flagged for inconsistencies are included in the average. As shown inthis example, a weighted average of the non-flagged development factorsin column (4) 1120 yields the average factor of 2.500 (value 1155); thatis, the average factor, 2.500, equals the sum of column (3) 1115 (value1160—9,103,455) divided by the sum of column (2) 1110 (value1165—3,641,378). Then the default 1st-to-2nd factor for Combo 70, wouldbe 0.81×2.5000=2.025 as shown in column (6) 1130. Thus, if the actualdata needed to calculate a 1^(st)-to-2^(nd) factor for this Combobecomes unusable due to a reporting inconsistency between the successiveannual statements, the default value of 2.025 may be used as a proxy forthe unusable factor.

For each entity in column (1) 1105, a default factor is calculated asthe product of the adjustment factor in column (5) 1125 and the averagefactor of 2.5 (value 1155). Each of the default factors are listed incolumn (6) 1130.

Continuing with the example of Combo 70 started above, it may beconsidered that the actual accident year 2011 1st-to-2nd factor forCombo 70 turns out to be 2.00000, so that the percent difference betweenactual and default is a deviation of 12.3%=(2.000000−2.025)/2.025. Asdescribed above, a default factor is estimated for each of the companiesthat have not been flagged and compared to the actual age-to-agefactors. The two observations with the largest deviations and the twowith the lowest are flagged. If an observation has been flagged, theage-to-age factor is set to the company default factor for that age(e.g., 2.6523 for Combo 914 in row 1170). The intent is to reduce thesensitivity of the index to extreme data points. Otherwise, theage-to-age factor is set to the observed factor (2.00 for Combo 70).Note that the default factor is sensitive to systemic risk since it isbased on the average factor for a group of companies.

In another example, two companies may merge or one company may acquireanother company. If the companies being merged are both in the referenceportfolio, age-to-age factors can be calculated based on the combinedentity. This entails constructing an as-if combined Schedule P Part Ifor the calendar year prior to the merger. For example, Company A mergeswith Company B during 2010. A combined Annual Statement in 2010 isfiled. For accident year 2009 the first annual statement in 2009 shows apaid loss of $2M of Company A and $3M for company B. For accident year2009, the second annual report in 2010 shows a paid loss of $6M for thecombined Company A+B. The 1st-to-2nd factor is thus $6M/5M=1.20. Thus,the deemed incremental paid for accident year 2009—calendar year 2010 iscalculated as cumulative deemed paid through 12/31/2009 times (1.20−1)which is $400K for A; $600K for B.

If one of the companies being merged is not in the reference portfoliobut files annual statements, age-to-age factors can be calculated basedon the combined entity. This entails constructing an as-if combinedSchedule P Part I for the calendar year preceding the merger. In somecases, companies may file both a post-merger consolidated annualstatement and individual company annual statements, making it possibleto calculate age-to-age factors for the companies originally in theportfolio. The principle is to use the figures that best match theoriginal entity. If the company being acquired is relatively small, theresulting distortion may be within the negotiated (e.g. 5%) tolerancelevel, resulting in a mechanical adjustment as described above.

If a company in the index stops reporting reliable annual statements dueto rehabilitation or liquidation, the calculation agent will select asimilar company or basket of companies of comparable volume to serve asa proxy in the calculation of age-to-age factors. Previously calculatedage-to-age factors remain unchanged.

If the calculation yields a negative incremental paid, the age-to-agefactor is flagged and deemed to be an error. The default age-to-agefactors for all company-age combinations are subject to a minimum ofunity.

It will be apparent to those skilled in the art that variousmodifications may be made in the present invention, without departingfrom the spirit or the scope of the invention. Thus, it is intended thatthe present invention cover modifications and variations of thisinvention provided they come within the scope of the appended claims andtheir equivalents.

1-24. (canceled)
 25. A method, comprising: calculating, by a processor,a first industry index amount at an index year based on (i) selectedactual loss values for the index year for a plurality of companies in adefined line of business, (ii) selected actual loss values for apredetermined number of years preceding the index year for the pluralityof companies in the defined line of business, and (iii) loss estimatesfor a number of years subsequent to the index year corresponding to apredetermined term of a systemic risk product for the plurality ofcompanies in the defined line of business; calculating, by theprocessor, a second industry index amount based on (i) the selectedactual loss values for the index year for the plurality of companies inthe defined line of business, (ii) the selected actual loss values forthe predetermined number of years preceding the index year for theplurality of companies in the defined line of business, and (iii)selected actual loss values for at least one year subsequent to theindex year for the plurality of companies in the defined line ofbusiness, wherein the at least one year subsequent to the index year isequal to the predetermined term of the systemic risk product;calculating, by the processor, an industry index value based on thefirst and second industry index amounts; and calculating a settlementamount based on the industry index value, an index trigger and an indexlimit.
 26. The method of claim 25, wherein the defined line of businessis based on a Schedule P defined line of business, wherein the ScheduleP is a National Association of Insurance Commissioners (NAIC), AnnualStatement schedule, wherein the Schedule P includes defined lines ofbusiness.
 27. The method of claim 25, wherein the selected actual lossvalues for the index year are one of actual paid loss values and casereserved loss values from Schedule P filings for the plurality ofcompanies, wherein the Schedule P filings are a National Association ofInsurance Commissioners (NAIC), Annual Statement schedule, wherein eachSchedule P includes ten years worth of paid loss data.
 28. The method ofclaim 25, wherein the predetermined term is any of one year to nineyears.
 29. The method of claim 25, wherein the selected actual lossvalues for the index year and the loss estimates are one of gross lossesor net losses.
 30. The method of claim 25, further comprising:determining a portion of the selected actual loss values for thepredetermined number of years preceding the index year for adjustmentbased on a consistency check; and adjusting, prior to calculating thefirst and second industry indices, the portion of the selected actualloss values for the predetermined number of years preceding the indexyear.
 31. The method of claim 25, wherein calculating the secondindustry index comprises: calculating an interim industry index amountbased on the selected actual loss values for the index year for theplurality of companies, the predetermined number of years preceding theindex year for the plurality of companies and at least one yearsubsequent to the index year; and calculating a final industry indexamount based on the selected actual loss values for the index year forthe plurality of companies, the predetermined number of years precedingthe index year for the plurality of companies and the number of yearssubsequent to the index year corresponding to the predetermined term ofthe systemic risk product, wherein the industry index value iscalculated based on the first, interim and final industry index amounts.32. A system, comprising: a memory storing a set of instructions; and aprocessor executing the set of instructions to perform operationscomprising: calculating a first industry index amount at an index yearbased on (i) selected actual loss values for the index year for aplurality of companies in a defined line of business, (ii) selectedactual loss values for a predetermined number of years preceding theindex year for the plurality of companies in the defined line ofbusiness, and (iii) loss estimates for a number of years subsequent tothe index year corresponding to a predetermined term of a systemic riskproduct for the plurality of companies in the defined line of business;calculating a second industry index amount based on (i) the selectedactual loss values for the index year for the plurality of companies inthe defined line of business, (ii) the selected actual loss values forthe predetermined number of years preceding the index year for theplurality of companies in the defined line of business, and (iii)selected actual loss values for at least one year subsequent to theindex year for the plurality of companies in the defined line ofbusiness, wherein the at least one year subsequent to the index year isequal to the predetermined term of the systemic risk product;calculating an industry index value based on the first and secondindustry index amounts; and calculating a settlement amount based on theindustry index value, an index trigger and an index limit.
 33. Thesystem of claim 32, wherein the defined line of business is based on aSchedule P defined line of business, wherein the Schedule P is aNational Association of Insurance Commissioners (NAIC), Annual Statementschedule, wherein the Schedule P includes defined lines of business. 34.The system of claim 32, wherein the selected actual loss values for theindex year are one of actual paid loss values and case reserved lossvalues from Schedule P filings for the plurality of companies, whereinthe Schedule P filings are a National Association of InsuranceCommissioners (NAIC), Annual Statement schedule, wherein each Schedule Pincludes ten years worth of paid loss data.
 35. The system of claim 32,wherein the predetermined term is any of one year to nine years.
 36. Thesystem of claim 32, wherein the selected loss actual values for theindex year and the loss estimates are one of gross losses or net losses.37. The system of claim 32, wherein the operations further comprise:determining a portion of the selected actual loss values for thepredetermined number of years preceding the index year for adjustmentbased on a consistency check; and adjusting, prior to calculating thefirst and second industry indices, the portion of the selected actualloss values for the predetermined number of years preceding the indexyear.
 38. The system of claim 32, wherein the operations furthercomprise: calculating an interim industry index amount based on theselected actual loss values for the index year for the plurality ofcompanies, the predetermined number of years preceding the index yearfor the plurality of companies and at least one year subsequent to theindex year; and calculating a final industry index amount based on theselected actual loss values for the index year for the plurality ofcompanies, the predetermined number of years preceding the index yearfor the plurality of companies and the number of years subsequent to theindex year corresponding to the predetermined term of the systemic riskproduct, wherein the industry index value is calculated based on thefirst, interim and final industry index amounts.
 39. A non-transitorycomputer readable storage medium with an executable program storedthereon, wherein the program instructs a processor to perform thefollowing steps: calculating a first industry index amount at an indexyear based on (i) selected actual loss values for the index year for aplurality of companies in a defined line of business, (ii) selectedactual loss values for a predetermined number of years preceding theindex year for the plurality of companies in the defined line ofbusiness, and (iii) loss estimates for a number of years subsequent tothe index year corresponding to a predetermined term of a systemic riskproduct for the plurality of companies in the defined line of business;calculating a second industry index amount based on (i) the selectedactual loss values for the index year for the plurality of companies inthe defined line of business, (ii) the selected actual loss values forthe predetermined number of years preceding the index year for theplurality of companies in the defined line of business, and (iii)selected actual loss values for at least one year subsequent to theindex year for the plurality of companies in the defined line ofbusiness, wherein the at least one year subsequent to the index year isequal to the predetermined term of the systemic risk product;calculating an industry index value based on the first and secondindustry index amounts, and calculating a settlement amount based on theindustry index value, an index trigger and an index limit.
 40. Thenon-transitory computer readable storage medium of claim 39, wherein thesteps further comprises: determining a portion of the selected actualloss values for the predetermined number of years preceding the indexyear for adjustment based on a consistency check; and adjusting, priorto calculating the first and second industry indices, the portion of theselected actual loss values for the predetermined number of yearspreceding the index year.
 41. The non-transitory computer readablestorage medium of claim 39, wherein the steps further comprise:calculating an interim industry index amount based on the selectedactual loss values for the index year for the plurality of companies,the predetermined number of years preceding the index year for theplurality of companies and at least one year subsequent to the indexyear; and calculating a final industry index amount based on theselected actual loss values for the index year for the plurality ofcompanies, the predetermined number of years preceding the index yearfor the plurality of companies and the number of years subsequent to theindex year corresponding to the predetermined term of the systemic riskproduct, wherein the industry index value is calculated based on thefirst, interim and final industry index amounts.